Smoothing Spline Method Research Articles

A modified algorithm of the combined ensemble empirical mode decomposition and independent component analysis for the removal of cardiac artifacts from neuromuscular electrical signals

Neuronal and muscular electrical signals contain useful information about the neuromuscular system, with which researchers have been investigating the relationship of various neurological disorders and the neuromuscular system. However, neuromuscular signals can be critically contaminated by cardiac electrical activity (CEA) such as the electrocardiogram (ECG) which confounds data analysis. The purpose of our study is to provide a method for removing cardiac electrical artifacts from the neuromuscular signals recorded. We propose a new method for cardiac artifact removal which modifies the algorithm combining ensemble empirical mode decomposition (EEMD) and independent component analysis (ICA). We compare our approach with a cubic smoothing spline method and the previous combined EEMD and ICA for various signal-to-noise ratio measures in simulated noisy physiological signals using a surface electromyogram (sEMG). Finally, we apply the proposed method to two real-life sets of data such as sEMG with ECG artifacts and ambulatory dog cardiac autonomic nervous signals measured from the ganglia near the heart, which are also contaminated with CEA. Our method can not only extract and remove artifacts, but can also preserve the spectral content of the neuromuscular signals.

Research on Fitting Method for Flow Characteristics of Small Injection Pulse Width of Injector

Due to the fact that it is generally difficult to accurately calculate the nonlinear section of flow characteristics curve of small injection pulse width of electronic control injector, it is impossible for electronic control unit (ECU) to accurately control fuel injection quantity when the small engine such as motorcycle is under a working condition of idle speed or small load. This paper introduces the principle and method to make a fitting for flow characteristics of nonlinear section in the developed software system in details. Take the electronic control injector of motorcycle as an example, the programming method combined with LabVIEW and MATLAB is utilized to make a fitting treatment for accurate fuel injection quantity obtained via measuring single-chip microcomputer through Smoothing Spline method, so as to obtain the flow characteristics of small injection pulse width and normal injection pulse width of electronic control injector of motorcycle.

Ultrasound based Strain Imaging Technique by 2D Thin Plate Smoothing Spline Method

Ultrasound based Strain Imaging Technique by 2D Thin Plate Smoothing Spline Method

Short crack initiation and growth kinetics analysis in a microalloyed steel plate using rotating bending fatigue modified notched specimens

Experimental microalloyed steel was tested employing samples with a suitable geometry for crack initiation and kinetics of short crack propagation monitoring through rotating bending fatigue constant loads. Trough the Finite Element Method (FEM) stress distribution was evaluated in pre-selected zones to establish the critical points for visual examination of the initiation cracks by optical microscopy. The experimental test loads were established between the fatigue and elastic limits. The short crack evolution was studied by means of the exponential crack growth law. It was shown that the initiation process of fatigue cracks is intensified gradually by the fatigue damage, featuring by the appearance of persistent slip bands, and the growth of short cracks mechanism is related to the coalescence of micro-cavities. Features of interaction between the surface cracks and steel microstructure are reported. The smoothing splines method was employ to analyze the kinetic crack growth data to establish a correlation between the crack length and crack growth rate. For the first time in this kind of steels, a relevant result is reported, the crack growth coefficient, Kg, that characterize their fatigue short crack growth under the influence of different constant loads.

Temporal Patterns of the Two-Dimensional Spatial Trends in Summer Temperature and Monsoon Precipitation of Bangladesh

Two climate indices, TXx and PRCPTOT, representing the summer maximum temperature and annual total monsoon precipitation, respectively, in Bangladesh were computed. The temperature and precipitation measurements from 34 meteorological stations during the temporal extent of 1948–2007 were applied for indices’ computation under thorough quality control. The spatial trends of the indices were analyzed by applying two-dimensional least square approach along latitudes and longitudes of the observation points. The temporal patterns of the spatial trends were identified by temporally interpolating them applying thin plate smoothing spline method. The analyses of TXx identified regional scale spatial trends in the east-west and south-north directions, which were increasing between 1948 and 1980s. After the 1980s the spatial trends started decreasing, and after 2000 the spatial trend along the south-north changed its direction to the north-south and continued until present. The analyses of the PRCPTOT identified spatial trends in the west-east and north-south directions, which were decreasing between 1948 and 1980s and thereafter increasing until present. About half of the spatial trends were significant in F-statistics at or more than 90% confidence level. Thus, the obtained results indicated a significant climatic shift within the regional scale of the country during the study period.

A Bayesian smoothing spline method for mortality modelling

AbstractWe propose a new method for two-dimensional mortality modelling. Our approach smoothes the data set in the dimensions of cohort and age using Bayesian smoothing splines. The method allows the data set to be imbalanced, since more recent cohorts have fewer observations. We suggest an initial model for observed death rates, and an improved model which deals with the numbers of deaths directly. Unobserved death rates are estimated by smoothing the data with a suitable prior distribution. To assess the fit and plausibility of our models we perform model checks by introducing appropriate test quantities. We show that our final model fulfils nearly all requirements set for a good mortality model.

Responsiveness of a semi-automated novel method of measuring cartilage loss in knee osteoarthritis over two years using 3.0T DESS 3D MRI

s / Osteoarthritis and Cartilage 20 (2012) S54–S296 S222 Further, no differences in the mean or SD signal intensity in any of the muscle regions were noted at baseline (data not shown). Changes in ACSAs over 2 years also did not significantly differ between progressor and non-progressor knees (Table 1). When stratifying comparisons for cases with little baseline pain (WOMAC score of 0-1; n1⁄47) vs. those with a score of 5-8 (n1⁄48), the findings were similar (data not shown). Conclusions: Progressor (case) and non-progressor (control) knees in this study were carefully selected from a large subsample, based on two independent measures of structural OA progression (MRI cartilage loss and JSW reduction in X-rays). Further, cases and controls were carefully matched for measures known to be associated with progression or with muscle area. The results of this exploratory study do not provide support that, once radiographic knee OA is established, baseline or longitudinal changes in thigh muscle ACSAs or strength predict (or are associated) with structural progression. 438 EVALUATION OF THE DEPENDENCY OF GLYCOSAMINOGLYCAN (GAG) CHEMICAL EXCHANGE SATURATION TRANSFER (GAGCEST) IMAGING ON CARTILAGE GAG CONTENT IN THE ANKLE AT 3 T B. Schmitt, M. Brix, J. Hofstaetter, R. Windhager, S. Trattnig, S. Domayer. Med. Univ. of Vienna, Vienna, Austria Purpose: This study was performed to evaluate the feasibility of gagCEST imaging in the ankle on a clinical 3-Tesla MR scanner. The dependency of gagCEST signal on cartilage GAG content was investigated by comparison of MRI data with quantitative biochemical assessment of cartilage GAG content. Methods: The study comprised 7 ankle samples from human cadavers, which were examined on a clinical 3 T MR System with a standard knee coil. PDw were acquired with turbo spin-echo (TSE) imaging and fatsat (FS) in the sagittal plane (TE1⁄426ms, TR1⁄44000ms, resolution1⁄40.4x0.4x3mm3). GagCEST imaging was performed using a segmented 3D RF-spoiled gradient-echo (GRE) sequence (TE1⁄43.49ms, TR 1⁄49.1ms, resolution1⁄40.6x0.6x3.3mm3, scan time 10:30 min). Selective RF presaturation was achieved using a series of 3 Gaussian RFPulses with pulse duration sp1⁄4100ms, an interpulse delay sd1⁄410ms and a B1 of 2.6mT. Z-spectra from images were corrected for B0 inhomogeneities on a pixel-by-pixel basis by a smoothing spline method. The asymmetry of the magnetization transfer rate (MTR) as determined by MTRasym (d) 1⁄4 MTR(+d)-MTR(-d) was integrated over the offset range from 0.5 2ppm, which corresponds to the resonance signal distribution from exchangeable GAG -OH protons, and used as signal intensity for gagCEST images. For quantitative biochemical analysis of absolute GAG content in cartilage, as gold standard, the tibial and talar cartilage compartments were divided into three segments (lateral, central, medial) with 1cm width in the sagittal plane (Fig. 1a). In each segment, 5 contiguous cartilage samples were taken, and a GAG assay (Blyscan B3000 GAG Assay) was used to determine absolute GAG content (mg/mg) and water content of the probes. The calculated GAG concentrations were expressed as the relative weight per cartilage wet weight [% GAG/mg WWt]. To compare MRI data to biochemical analysis, cartilage areas were segmented in MR images and gagCEST values were averaged in regions corresponding to the division used for biochemical analysis. The correlation coefficient (r) for gagCEST and biochemical essay was determined using Pearson correlation analysis. To account for individual differences in cartilage water content, which can alter chemical exchange effects, measured gagCEST signals were scaled to the fictive case of 90 % water content in cartilage. Results: All examined ankles showed morphologically intact cartilage on PDw MR images. From the 42 available cartilage samples (7 patients x 2 cartilage surfaces x 3 cartilage segments 1⁄4 42), 4 samples from ankle # 6 were excluded from analysis due to extremely thin (<< 0.8 mm) cartilage in the medial and lateral segments. The remaining 38 data points showed a linear correlation between gagCEST signal intensities and GAG concentrations with r 1⁄4 0.797 if differences in water contents were neglected. If these differences were accounted for, a higher correlation coefficient of r 1⁄40.859 was obtained (Fig. 1b). The average measured gagCEST signal intensity (Fig. 1c) was 5.47 3.52 % (mean SD), and 8.11 5.32 % with normalized water content. The average GAG content as determined by biochemical analysis was 6.49 1.14 % GAG/mg WWt. The relative water content in cartilage had a mean of 68.85 4.54 %.

The Estimation of Smoothing Parameter using Smoothing Techniques

This article discusses on the smoothing parameter which is controlled by interpolating spline basedon the smoothing techniques that consisted of smoothing spline method, kernel regression method, andpenalized spline regression method.The smoothing parameter is controlled the fitting model and the trade of between the bias of theestimator. We also propose the range of smoothing parameter of these methods to fit the smoothing functionwhich data is nonlinear. Therefore, we mention the characteristic of smoothing function when the smoothingparameters have the various values. According to the results, it is concluded that the smoothing parameterof the smoothing spline method is suitable worked between zero to one, the kernel regression is goodperformance between two to ten, and the penalized spline is useful between one to ten. Key Words : Smoothing Parameter; Smoothing Technique; Smoothing Spline; Kernel Regression; PenalizedSpline Regression

Potential and limitations of using satellite data to evaluate the spatial detail in climatological air temperature maps

Detailed patterns of spatial variability in surface temperature can be observed with the use of thermal infrared data from satellites. A method is developed to use clear‐sky thermal infrared satellite data to evaluate traditional monthly average maximum air temperature maps interpolated from observations at surface stations using a statistical thin plate smoothing spline method. Results of comparisons over Alberta, Manitoba and Saskatchewan from June to October, for the years 2001 to 2005, are presented. The satellite data allow identification of some limitations in the interpolation technique at high altitudes in mountain ranges and in data‐sparse areas due to low station density. In the data‐sparse areas, the highest discrepancies could be linked to the unrepresentativeness of the stations because of different land cover or the presence of water bodies. Conversely, the interpolated air temperature maps allow the identification of problems with using thermal infrared data to estimate near‐surface air temperatures in areas of significant moisture deficit and at the locations of water bodies.

Smoothing Spline Estimation for Partially Linear Single-index Models

In this article, the partially linear single-index models are discussed based on smoothing spline and average derivative estimation method. This proposed technique consists of two stages: one is to estimate the vector parameter in the linear part using the smoothing cubic spline method, simultaneously, obtaining the estimator of unknown single-index function; the other is to estimate the single-index coefficients in the single-index part by the using average derivative estimator procedure. Some simulated and real examples are presented to illustrate the performance of this method.

Methodologies to Predict Service Lives of Pavement Marking Materials

This study focuses on developing methodologies to predict the service life of a pavement marking material based on its retroreflectivity. Data from the 2002 National Transportation Product Evaluation Program (NTPEP) pavement marking material test deck in Mississippi are used for model development and model validation. The smoothing spline method and time series modeling are applied to estimate the service lives of different types of materials based on the assumption of a required minimum retroreflectivity value. The same models can also predict the retroreflectivity values at future times for a pavement marking product based on its retroreflectivity values in the past. The validation of the models shows satisfactory accuracy. As demonstrated in a case study, the predicted service lives of the marking materials can be used in life-cycle cost comparisons for selecting pavement marking material.

Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters

This paper considers the problem of estimating curve and surface functions when the structures of an unknown function vary spatially. Classical approaches such as using smoothing splines, which are controlled by a single smoothing parameter, are inefficient in estimating the underlying function that consists of different spatial structures. In this paper, we propose a blockwise method of fitting smoothing splines wherein the smoothing parameter λ varies spatially, in order to accommodate possible spatial nonhomogeneity of the regression function. A key feature of the proposed blockwise method is the parameterization of a smoothing parameter function λ ( x ) that produces a continuous spatially adaptive fit over the entire range of design points. The proposed parameterization requires two important ingredients: (1) a blocking scheme that divides the data into several blocks according to the degree of spatial variation of the data; and (2) a method for choosing smoothing parameters of blocks. We propose a block selection approach that is based on the adaptive thinning algorithm and a choice of smoothing parameters that minimize a newly defined blockwise risk. The results obtained from numerical experiments validate the effectiveness of the proposed method.

Age Dependence of the Risk of Intussusception Following Tetravalent Rhesus-Human Reassortant Rotavirus Tetravalent Vaccine: Is It Beyond Doubt?

The relation between the risk of intussusception and age at the time of receipt of the first dose of rhesus-human reassortant rotavirus tetravalent vaccine (RRV-TV) has been studied extensively on the basis of Centers for Disease Control and Prevention (CDC) matched case-control study data, using various statistical methods, including conditional logistic regression and quadratic smoothing splines. However, different conclusions have been reported in published analyses regarding the dependence of the risk of intussusception on age at first dose. The authors reanalyzed the CDC matched case-control data set using unrestricted and restricted quadratic smoothing spline methods for various exposure windows (i.e., intervals postvaccination). These analyses indicated that the use of different models may lead to different conclusions. The restricted quadratic smoothing spline with appropriately chosen knot locations showed a statistically significant increased risk of intussusception associated with RRV-TV for the exposure window 3-14 days after the first dose at an age as young as 49 days, the youngest age in the data set at which vaccine was administered; this implies an increased risk of intussusception associated with RRV-TV at all ages studied.

Scattered data reconstruction by regularization in B-spline and associated wavelet spaces

The problem of fitting a nice curve or surface to scattered, possibly noisy, data arises in many applications in science and engineering. In this paper we solve the problem using a standard regularized least square framework in an approximation space spanned by the shifts and dilates of a single compactly supported function ϕ . We first provide an error analysis to our approach which, roughly speaking, states that the error between the exact (probably unknown) data function and the obtained fitting function is small whenever the scattered samples have a high sampling density and a low noise level. We then give a computational formulation in the univariate case when ϕ is a uniform B-spline and in the bivariate case when ϕ is the tensor product of uniform B-splines. Though sparse, the arising system of linear equations is ill-conditioned; however, when written in terms of a short support wavelet basis with a well-chosen normalization, the resulting system, which is symmetric positive definite, appears to be well-conditioned, as evidenced by the fast convergence of the conjugate gradient iteration. Finally, our method is compared with the classical cubic/thin-plate smoothing spline methods via numerical experiments, where it is seen that the quality of the obtained fitting function is very much equivalent to that of the classical methods, but our method offers advantages in terms of numerical efficiency. We expect that our method remains numerically feasible even when the number of samples in the given data is very large.

Spline Smoothing Over Difficult Regions

We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over and across difficult regions. More unfavorable properties of standard smoothers become visible when the data is observed on an irregular grid in a non-rectangular domain. In this paper, we adopt smoothing spline methods within a state space framework to smooth data on one- or two-dimensional grids with difficult regions. We make a distinction between two types of missing observations to handle the irregularity of the grid and to ensure that no smoothing takes place over and across the difficult region. For smoothing on two-dimensional grids, we introduce a two-step spline smoothing method. The proposed solution applies to all smoothing methods that can be represented! in a state space framework. We illustrate our methods for three different cases of interest.

Stabilizing of an ill-posed inverse problem by using smoothing splines and hyperbolic heat equation

A smoothing splines method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model. The recovery of initial profile with parabolic model is extremely ill-posed and it is desirable to develop a method to recover some useful information about the initial profile. It is demonstrated in this article that the recovery of the initial profile by a parabolic model is impossible in case of corrupted data, however, it is possible to recover the initial profile in a stable way by reformulating the problem by a hyperbolic model together with a smoothing splines method. One example is used for comparison of parabolic model and the proposed model for different modes and time displacements. A graphical comparison is given between the proposed model and the parabolic model.

A Functional Wavelet–Kernel Approach for Time Series Prediction

SummaryWe consider the prediction problem of a time series on a whole time interval in terms of its past. The approach that we adopt is based on functional kernel nonparametric regression estimation techniques where observations are discrete recordings of segments of an underlying stochastic process considered as curves. These curves are assumed to lie within the space of continuous functions, and the discretized time series data set consists of a relatively small, compared with the number of segments, number of measurements made at regular times. We estimate conditional expectations by using appropriate wavelet decompositions of the segmented sample paths. A notion of similarity, based on wavelet decompositions, is used to calibrate the prediction. Asymptotic properties when the number of segments grows to ∞ are investigated under mild conditions, and a nonparametric resampling procedure is used to generate, in a flexible way, valid asymptotic pointwise prediction intervals for the trajectories predicted. We illustrate the usefulness of the proposed functional wavelet–kernel methodology in finite sample situations by means of a simulated example and two real life data sets, and we compare the resulting predictions with those obtained by three other methods in the literature, in particular with a smoothing spline method, with an exponential smoothing procedure and with a seasonal autoregressive integrated moving average model.

Component selection and smoothing in multivariate nonparametric regression

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The “COSSO” is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent proposals for model selection in linear models and smoothing spline ANOVA models. Theoretical properties, such as the existence and the rate of convergence of the COSSO estimator, are studied. In the special case of a tensor product design with periodic functions, a detailed analysis reveals that the COSSO does model selection by applying a novel soft thresholding type operation to the function components. We give an equivalent formulation of the COSSO estimator which leads naturally to an iterative algorithm. We compare the COSSO with MARS, a popular method that builds functional ANOVA models, in simulations and real examples. The COSSO method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets. The COSSO gives very competitive performance in these studies.

Phase retrieval in digital speckle pattern interferometry by application of two-dimensional active contours called snakes

We propose a novel approach to retrieving the phase map coded by a single closed-fringe pattern in digital speckle pattern interferometry, which is based on the estimation of the local sign of the quadrature component. We obtain the estimate by calculating the local orientation of the fringes that have previously been denoised by a weighted smoothing spline method. We carry out the procedure of sign estimation by determining the local abrupt jumps of size pi in the orientation field of the fringes and by segmenting the regions defined by these jumps. The segmentation method is based on the application of two-dimensional active contours (snakes), with which one can also estimate absent jumps, i.e., those that cannot be detected from the local orientation of the fringes. The performance of the proposed phase-retrieval technique is evaluated for synthetic and experimental fringes and compared with the results obtained with the spiral-phase- and Fourier-transform methods.

Evaluating Implied RNDs by Some New Confidence Interval Estimation Techniques

This paper evaluates the precision of the parametric double lognormal (DLN) and the nonparametric smoothing spline method (SPLINE) for estimating risk-neutral distributions (RNDs) from observed option prices. By using a bootstrap technique confidence bands are estimated for the riskneutral distributions (RNDs) and the width is used as the criterion when evaluating the precision of the two. Previous literature on estimating confidence bands has to a large extent been estimated by Monte Carlo methods. We argue that the bootstrap technique is to be preferred due to the non-normality of the error structure. Our findings favour the SPLINE method, yielding tighter confidence bands. An example showing how the confidence intervals could be used for practical purposes is also provided.